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Q.

If P represents radiation pressure, C speed of light, and Q radiation energy striking unit area per second and x,y,z are non zero integers, then P^x Q^y C^z is dimensionless. The values of x,y and z are respectively

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a

1,1,-1

b

1,-1,1

c

-1,1,1

d

1,1,1

answer is B.

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Detailed Solution

$\begin{array}{l} P^{x} Q^{y} c^{z} = M^{0} L^{0} T^{0} \\ p = [{ML}^{- 1} T^{- 2}]; c = [{LT}^{- 1}]; Q = [{MT}^{- 3}] \\ {[{ML}^{- 1} T^{- 2}]}^{x} {[{ML}^{- 3}]}^{y} {[{LT}^{- 1}]}^{z} = M^{0} L^{0} T^{0} \\ M^{x + y} L^{- x + z} T^{- 2 x - 3 y - z} = M^{0} L^{0} T^{0} \\ x + y = 0 \Rightarrow y = - x \Rightarrow - x + z = 0 \Rightarrow x = z \\ - 2 x - 3 y - z = 0 \end{array}$
if as x, y, z ar non zero the equation are satisfied when
x=1 ; y=-1 ; z=1

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